0.84 g of a metal carbonate reacts exactly with 40 ml of N/2 `H_(2)SO_(4)`. The equivalent weight of the metal carbonate

Options

A. 84
B. 64
C. 42
D. 32

Explanation

To find the equivalent weight of the metal carbonate, we can follow these steps:

### Step 1: Calculate the Normality of H₂SO₄
Given that we have 40 ml of N/2 H₂SO₄, we can convert this to normality:
- Normality (N) = N/2 = 0.5 N

### Step 2: Calculate the Molarity of H₂SO₄
Normality is related to molarity (M) by the formula:
\[ \text{Normality} = \text{Molarity} \times \text{Valence Factor} \]
For H₂SO₄, the valence factor is 2 (since it can donate 2 protons).
Thus:
\[ 0.5 = M \times 2 \]
\[ M = \frac{0.5}{2} = 0.25 \, \text{M} \]

### Step 3: Calculate Moles of H₂SO₄
Using the molarity and the volume of H₂SO₄, we can find the number of moles:
\[ \text{Moles of H₂SO₄} = \text{Molarity} \times \text{Volume in Liters} \]
Convert 40 ml to liters:
\[ 40 \, \text{ml} = \frac{40}{1000} = 0.04 \, \text{L} \]
Now calculate the moles:
\[ \text{Moles of H₂SO₄} = 0.25 \, \text{M} \times 0.04 \, \text{L} = 0.01 \, \text{moles} \]

### Step 4: Calculate the Weight of H₂SO₄
To find the weight of H₂SO₄, we multiply the moles by the molar mass of H₂SO₄:
- Molar mass of H₂SO₄ = 2(1) + 32 + 4(16) = 98 g/mol
\[ \text{Weight of H₂SO₄} = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Weight of H₂SO₄} = 0.01 \, \text{moles} \times 98 \, \text{g/mol} = 0.98 \, \text{g} \]

### Step 5: Calculate the Equivalent Weight of H₂SO₄
The equivalent weight of H₂SO₄ can be calculated using:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{\text{Valence Factor}} \]
\[ \text{Equivalent Weight of H₂SO₄} = \frac{98}{2} = 49 \, \text{g/equiv} \]

### Step 6: Set Up the Equivalence Equation
Since the equivalence of metal carbonate is equal to the equivalence of H₂SO₄, we can write:
\[ \text{Equivalence of H₂SO₄} = \text{Equivalence of Metal Carbonate} \]

Using the formula for equivalence:
\[ \text{Equivalence} = \frac{\text{Mass}}{\text{Equivalent Weight}} \]
For H₂SO₄:
\[ \text{Equivalence of H₂SO₄} = \frac{0.98 \, \text{g}}{49 \, \text{g/equiv}} = 0.02 \, \text{equiv} \]

### Step 7: Calculate the Equivalent Weight of Metal Carbonate
Let the equivalent weight of the metal carbonate be \( E \):
\[ \text{Equivalence of Metal Carbonate} = \frac{0.84 \, \text{g}}{E} \]
Setting the equivalences equal:
\[ \frac{0.98}{49} = \frac{0.84}{E} \]

Cross-multiplying gives:
\[ 0.98E = 0.84 \times 49 \]
\[ E = \frac{0.84 \times 49}{0.98} \]

### Step 8: Solve for E
Calculating the right side:
\[ E = \frac{41.16}{0.98} \approx 42 \, \text{g/equiv} \]

### Conclusion
The equivalent weight of the metal carbonate is **42 g/equiv**.

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